Twin lattice - Revision history

BrianMcMahon: Tidied translations and added German and Spanish (U. Mueller)

2017-11-20T14:13:55Z

Tidied translations and added German and Spanish (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-17T13:59:54Z

Style edits to align with printed edition

MassimoNespolo: link

2015-04-05T09:15:25Z

link

MassimoNespolo at 17:34, 15 April 2007

2007-04-15T17:34:50Z

MassimoNespolo at 17:04, 15 April 2007

2007-04-15T17:04:43Z

MassimoNespolo at 09:41, 15 May 2006

2006-05-15T09:41:55Z

MassimoNespolo at 10:57, 7 May 2006

2006-05-07T10:57:37Z

MassimoNespolo at 08:47, 7 May 2006

2006-05-07T08:47:43Z

MassimoNespolo: /* Twin lattice */

2006-05-07T08:47:03Z

‎Twin lattice

MassimoNespolo: (Fr)

2006-05-07T08:43:18Z

(Fr)

← Older revision		Revision as of 14:13, 20 November 2017
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−	<~~Font~~ color="blue"> Réseau de la macle</~~Font~~> (''Fr''). <~~Font~~ color="black"> Reticolo del geminato </~~Font~~>(''It''). <~~Font~~ color="purple"> 双晶格子 </~~Font~~>(''Ja'').	+	<font color="blue">Réseau de la macle</font> (''Fr''). <font color="red">Zwillingsgitter</font> (''Ge''). <font color="black">Reticolo del geminato</font> (''It''). <font color="purple">双晶格子</font> (''Ja''). <font color="green">Red de la macla</font> (''Sp'').
		+

	A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are [[twinning (effects of)\|overlapped (restored)]] to some extent. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface.		A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are [[twinning (effects of)\|overlapped (restored)]] to some extent. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface.

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-<Font color="blue"> Réseau de la macle</Font> (''Fr''). <Font color="black"> Reticolo del geminato </Font>(''It''). <Font color="purple"> 双晶格子 </Font>(''Ja'')
+<Font color="blue"> Réseau de la macle</Font> (''Fr''). <Font color="black"> Reticolo del geminato </Font>(''It''). <Font color="purple"> 双晶格子 </Font>(''Ja'').
 A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are [[twinning (effects of)|overlapped (restored)]] to some extent. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface.
-Let H* = &cap;<sub>i</sub>H<sub>i</sub> be the intersection group of the individuals in their respective orientations, D(H*) the holohedral supergroup (proper or trivial) of H*, D('''L'''<sub>T</sub>) the point group of the twin lattice and D('''L'''<sub>ind</sub>) the point group of the individual lattice. D('''L'''<sub>T</sub>) either coincides with D(H*) (case of zero [[twin obliquity]]) or is a proper supergroup of it (case of non-zero [[twin obliquity]]): it can be higher, equal or lower than D('''L'''<sub>ind</sub>).
+Let ''H''* = &cap;<sub>''i''</sub>''H''<sub>''i''</sub> be the intersection group of the individuals in their respective orientations, ''D''(''H''*) the holohedral supergroup (proper or trivial) of ''H''*, ''D''('''L'''<sub>''T''</sub>) the point group of the twin lattice and ''D''('''L'''<sub>''ind''</sub>) the point group of the individual lattice. ''D''('''L'''<sub>''T''</sub>) either coincides with ''D''(''H''*) (case of zero [[twin obliquity]]) or is a proper supergroup of it (case of non-zero [[twin obliquity]]): it can be higher than, equal to or lower than ''D''('''L'''<sub>''ind''</sub>).
-*When D('''L'''<sub>T</sub>) = D('''L'''<sub>ind</sub>) and the two lattices have the same orientation, twinning is by [[twinning by merohedry|merohedry]] ([[twin index]] = 1). When at least some of the symmetry elements of D('''L'''<sub>T</sub>) are differently oriented from the corresponding ones of D('''L'''<sub>ind</sub>), twinning is by [[twinning by reticular polyholohedry|reticular polyholohedry]] ([[twin index]] > 1, [[twin obliquity]] = 0) or reticular pseudopolyholohedry ([[twin index]] > 1, [[twin obliquity]] > 0).
+*When ''D''('''L'''<sub>''T''</sub>) = ''D''('''L'''<sub>''ind''</sub>) and the two lattices have the same orientation, twinning is by [[twinning by merohedry|merohedry]] ([[twin index]] = 1). When at least some of the symmetry elements of ''D''('''L'''<sub>''T''</sub>) are differently oriented from the corresponding ones of ''D''('''L'''<sub>''ind''</sub>), twinning is by [[twinning by reticular polyholohedry|reticular polyholohedry]] ([[twin index]] > 1, [[twin obliquity]] = 0) or reticular pseudopolyholohedry ([[twin index]] > 1, [[twin obliquity]] > 0).
-*When D('''L'''<sub>T</sub>) &ne; D('''L'''<sub>ind</sub>) twinning is by [[twinning by pseudomerohedry|pseudomerohedry]] ([[twin index]] = 1, [[twin obliquity]] > 0), [[twinning by reticular merohedry|reticular merohedry]] ([[twin index]] > 1, [[twin obliquity]] = 0) or [[twinning by reticular pseudomerohedry|reticular pseudomerohedry]] ([[twin index]] > 1, [[twin obliquity]] > 0).
+*When ''D''('''L'''<sub>''T''</sub>) &ne; ''D''('''L'''<sub>''ind''</sub>) twinning is by [[twinning by pseudomerohedry|pseudomerohedry]] ([[twin index]] = 1, [[twin obliquity]] > 0), [[twinning by reticular merohedry|reticular merohedry]] ([[twin index]] > 1, [[twin obliquity]] = 0) or [[twinning by reticular pseudomerohedry|reticular pseudomerohedry]] ([[twin index]] > 1, [[twin obliquity]] > 0).
 ==History==
-The definition of twin lattice was given in: Donnay, G. ''Width of albite-twinning lamellae'', Am. Mineral., '''25''' (1940) 578-586, where the case D('''L'''<sub>T</sub>) &sub; D('''L'''<sub>ind</sub>) was however overlooked.
+The definition of twin lattice was given by G. Donnay [(1940). ''Am. Mineral.'' '''25''', 578-586. ''Width of albite-twinning lamellae''] where the case ''D''('''L'''<sub>''T''</sub>) &sub; ''D''('''L'''<sub>''ind''</sub>) was however overlooked.
 ==See also==
-Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>
+*[[Mallard's law]]
 [[Category:Twinning]]

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 <Font color="blue"> Réseau de la macle</Font> (''Fr''). <Font color="black"> Reticolo del geminato </Font>(''It''). <Font color="purple"> 双晶格子 </Font>(''Ja'')
-A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface.
+A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are [[twinning (effects of)|overlapped (restored)]] to some extent. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface.
 Let H* = &cap;<sub>i</sub>H<sub>i</sub> be the intersection group of the individuals in their respective orientations, D(H*) the holohedral supergroup (proper or trivial) of H*, D('''L'''<sub>T</sub>) the point group of the twin lattice and D('''L'''<sub>ind</sub>) the point group of the individual lattice. D('''L'''<sub>T</sub>) either coincides with D(H*) (case of zero [[twin obliquity]]) or is a proper supergroup of it (case of non-zero [[twin obliquity]]): it can be higher, equal or lower than D('''L'''<sub>ind</sub>).

← Older revision		Revision as of 17:34, 15 April 2007
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−	<Font color="blue"> Réseau de la macle</Font> (''Fr''). <Font color="black"> Reticolo del geminato </Font>(''It''). <Font color="purple"> ~~晶双格子~~ </Font>(''Ja'')	+	<Font color="blue"> Réseau de la macle</Font> (''Fr''). <Font color="black"> Reticolo del geminato </Font>(''It''). <Font color="purple"> 双晶格子 </Font>(''Ja'')

	A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface.		A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface.

← Older revision		Revision as of 17:04, 15 April 2007
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−	<Font color="blue"> Réseau de la macle</Font> (''Fr'') <Font color="black"> Reticolo del geminato </Font>(''It'')	+	<Font color="blue"> Réseau de la macle</Font> (''Fr''). <Font color="black"> Reticolo del geminato </Font>(''It''). <Font color="purple"> 晶双格子 </Font>(''Ja'')

	A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface.		A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface.

← Older revision		Revision as of 09:41, 15 May 2006
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	Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>		Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>

−	[[Category:~~Fundamental crystallography~~]]	+	[[Category:Twinning]]

← Older revision		Revision as of 08:47, 7 May 2006
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−	<Font color="blue"> Réseau de la macle</Font>(''Fr'') <Font color="black"> Reticolo del geminato </Font>(''It'')	+	<Font color="blue"> Réseau de la macle</Font> (''Fr'') <Font color="black"> Reticolo del geminato </Font>(''It'')
−
−	~~= Twin lattice =~~

	A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. It corresponds to the crystal lattice in [[twinning by merohedry]] and to a sublattice of the crystal (individual) in [[twinning by reticular merohedry]].		A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. It corresponds to the crystal lattice in [[twinning by merohedry]] and to a sublattice of the crystal (individual) in [[twinning by reticular merohedry]].

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 = Twin lattice =
-A [[twinning|twin]] operation overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. It corresponds to the crystal lattice in [[twinning by merohedry]] and to a sublattice of the crystal (individual) in [[twinning by reticular merohedry]].
+A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. It corresponds to the crystal lattice in [[twinning by merohedry]] and to a sublattice of the crystal (individual) in [[twinning by reticular merohedry]].
 Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>
 [[Category:Fundamental crystallography]]